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Conic Section
Question
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If the lines 3x − 4y − 7 = 0 and 2x − 3y − 5 = 0 are two diameters of a circle of area 49π square units, the equation of the circle is

  • x2 + y2 + 2x − 2y − 47 = 0

  • x2 + y2 + 2x − 2y − 62 = 0

  • x2 + y2 − 2x + 2y − 62 = 0

  • x2 + y2 − 2x + 2y − 47 = 0

Answer

D.

x2 + y2 − 2x + 2y − 47 = 0

Point of intersection of 3x − 4y − 7 = 0 and 2x − 3y − 5 = 0 is (1 , − 1), which is the centre of the circle and radius = 7.
∴ Equation is (x − 1)2 + (y + 1)2 = 49
⇒ x2 + y2 − 2x + 2y − 47 = 0.

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If the lines 3x − 4y − 7 = 0 and 2x − 3y − 5 = 0 are two diameters of a circle of area 49π square units, the equation of the circle is